Question

1.) find the sum of this infinite geometric series 12+4+4/3+...
2.) Find the value of S for and infinite geometric series with r=1/6 and a1=10
3.)Find the sum of this infinite geometric series 8+4+2+...
4.)Find the value of r for an infinite geometric series with S = 96 and a1=12

Answer 1

Step one: apply the following formula:

Answer 2

\[S_{\infty} = \frac{ a _{1} }{ 1-r }\] one: apply the following formula:

Answer 3

Step two: figure out what is a1 and r!

Answer 4

for the first question a1= 12, r= 1/3, then plug those values in the formula about you get the infinite sum of the GS

Answer 5

you repeat the same process for part 2 and part 3

Answer 6

in part for you have the value of the sum and a1 so find r, i will show you how to rearrange the formula

Answer 7

r = 1- a1/S

Answer 8

now all you need to do is plug in the numbers to get the right answer

Answer 9

How we figure the value of r from a series?

Answer 10

well take the next term and divide by the first one you get the value of r, for example in the first part you got 12+4+4/3 .... this means we can take 4 which is the next term and divide it by 12 to obtain the value of r which is 1/3

Answer 11

similarly the value of r for the the 3rd part would be 4/8=1/2=r

Answer 12

i hope this helps

Answer 13

all the best